1. Math Forum: Finding The Value Of Pi But one problem remained what is the numerical value of pi? to Euler s Solutionof the Bridges to a Chronological Table of the Values Attributed to Pi http://mathforum.org/isaac/problems/pi1.html

Finding the Value of Pi A Math Forum Project Table of Contents: Famous Problems Home The Bridges of Konigsberg The Value of Pi Prime Numbers ... Links Historians estimate that by 2000 B.C. humans had noticed that the ratio of circumference to diameter was the same for all circles. This discovery hinged on the idea of proportion - in this case humans noticed that if you double the distance "across" a circle, then you double the distance "around" it. In today's algebraic notation this implied the formula where Pi was constant. (It wasn't until 1706 that this notation, using the Greek letter seen in the above equation - often written Pi and pronounced like the English 'pie' - was introduced by William Jones). The significance of this discovery is clear: Circles are everywhere - in the sun, the moon, the pupils of our eyes, the most basic religious rituals and the earliest man-made structures. Achieving a greater mathematical understanding of Pi would lead to scientific and technological advances that would further the development of civilization, as well as creating some very interesting problems in pure mathematics. But one problem remained - what is the numerical value of Pi?

2. The Pi-Search Page The maximum number of digits of Pi necessary to find any monthday combination is 60872. Interestingly enough, this is the same value with http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. About "Finding The Value Of Pi" Finding the value of pi. _ Library Home Full Table of Contents Suggest a Link Library Help http://mathforum.org/library/view/7473.html

Finding the Value of Pi Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://mathforum.org/isaac/problems/pi1.html Author: Isaac Reed Description: Throughout the history of civilization various mathematicians have been concerned with discovering the value of and different expressions for the ratio of the circumference of a circle to its diameter. Levels: High School (9-12) College Languages: English Resource Types: Problems/Puzzles Math Topics: Pi Home The Math Library Quick Reference ... Help http://mathforum.org/

4. Math Forum Finding The Value Of Pi Finding the value of pi. A Math Forum Project. Table of Contents Famous Problems Home http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. Discovering The Value Of Pi A lesson that uses an applet to allow the student to measure many circles andfigure out the fact that Pi exists and its value. http://www.arcytech.org/java/pi/

Discovering the Value of Pi ( The purpose of this lesson is for you to discover a very special attribute of circles. Preface Measuring Circles Analyzing the Data Interesting facts about Pi ... Lesson Description (for Teacher) Last Updated: Saturday, 10-Mar-2001 02:02:09 GMT Arcytech Java Home Page Provide ... Feedback

6. Discovering The Value Of Pi A lesson that uses an applet to allow the student to measure many circles and figure out the fact that Pi exists and its value. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. Lesson Description For Teachers By doing so, they should discover the approximate value of pi. By discovering iton their own they should feel rewarded and gain a deeper understanding of http://www.arcytech.org/java/pi/teachers.html

Lesson Description for Teachers Summary: The students use a Java Applet to discover the fact that the ratio of the circumference to the diameter is a constant that applies to all circles. In other words, it teaches them the concept of pi and how it is derived. The lesson also includes a sheet with interesting facts about pi. Grade Level: th to 12 th Objectives: The students will measure the diameter and circumference of many circles and will estimate their relationship. By doing so, they should discover the approximate value of pi. By discovering it on their own they should feel rewarded and gain a deeper understanding of the fundamental concept of pi. Materials: None other than a computer with internet access. They might not even need pencil and paper as they can fill out the data table on the computer. Procedure: This lesson is completely self guided and the students can do it on their own. You could assign it as a homework and have a meaningful discussion the next day or do it during class. Even though everything is explained within the lesson, you may want to describe (or review) what the circumference and diameter of a circle are and show them (with the applet or with a similar method) how can one measure both quantities. Ask them if they think there is a relationship between the two, what that might be, if it holds true for all circles, etc. Next you may want to divide them in groups of 2 to 3 students (if you do not have enough computers) and tell them to go through the lesson, measure about 10 different size circles, and complete the first two columns in the table. All of this is described in the

8. The Pi Pages "The story of pi reflects the most seminal, the most serious and sometimes the silliest aspects of mathematics. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. How Is The Exact Value Of Pi Determined? Ask the experts your physics and astronomy questions, read answer archive, and more. http://www.physlink.com/Education/AskExperts/ae65.cfm

Not a member yet? Get Free Membership Username: Password: Remember me Forgot your login? Ask the Experts Physics ... eStore Question How is the exact value of pi determined? Asked by: Charlie Hinkle Answer The value of pi is the ratio of the circumference of a circle to its diameter . Therefore, you can determine the value of pi by drawing ANY perfect circle (either physically or in a computer program simulation), then measure it's circumference and diameter, take the ratio and that's it! The value of pi correct to seven decimal places is: . Pi is an irrational number, i.e. it cannot be expressed by a whole number or a common fraction. According to Encarta Encyclopedia pi has been worked out to a million decimal places by a computer without coming to a whole fraction. Answered by: Doris Thomas and Anton Skorucak go to the top Advertisement: '1995-'2005 PhysLink.com

10. Yet Another Story Of Pi (Sadly, many people would believe my calculator) Currently the value of pi is known to 6.4 billion places, but I won't attempt writing them out! http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. The Amazing History Of Pi This yields an approximate value of 3.1605 for pi. The first theoretical calculationof a value of pi was that of Archimedes of Syracuse (287212 BCE), http://www.ualr.edu/~lasmoller/pi.html

Did you know . . .? has a long and interesting history! Ancient history More pi history A novel way to compute pi- The symbol for pi ... For more information That the ratio of the circumference to the diameter of a circle is constant (namely, pi) has been recognized for as long as we have written records. A ratio of 3:1 appears in the following biblical verse: And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about. (I Kings 7, 23; II Chronicles 4, 2.) The ancient Babylonians generally calculated the area of a circle by taking 3 times the square of its radius ( =3), but one Old Babylonian tablet (from ca. 1900-1680 BCE) indicates a value of 3.125 for pi. Ancient Egyptians calculated the area of a circle by the following formula (where d is the diameter of the circle): This yields an approximate value of 3.1605 for pi. Beginning with a hexagon, he worked all the way up to a ploygon with 96 sides! Archimedes's method for approximating the value of pi.

12. Buffon's Needle 2. After 264 drops, the estimate of pi is 3.142857. This estimate is correct to within 2/1000 of the book value of pi. Will the next drop http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. ABC News Japanese Man Sets Record In Pi Recitation Akira Haraguchi, 59, had begun his attempt to recall the value of pi a mathematical value that has an infinite number of decimal places at a http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

14. The Ridiculously Enhanced Pi Page Information on links for Pi Day. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

15. Hidden Codes In The Bible: The Value Of Pi Hidden Codes in the Bible. The value of pi PI AND RANDOM NUMBERS. Pi isa quark of mathematics it is one of the basic building blocks out of which http://www.ldolphin.org/pi/

Personal Update, April 1998 Hidden Codes in the Bible: The Value of Pi by Chuck Missler Koinonia House Ministries When I was a teenager, I was confronted by a skeptic (a Unitarian, actually) concerning an apparent discrepancy in 1 Kings 7:23. This passage deals with Solomon's Temple and the products of Hiram the Bronzeworker: And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about. (1 Kings 7:23) The huge cast bronze basin in 1 Kings 7:23 was 10 cubits (note 1) in diameter and its circumference was 30 cubits, which is mathematically inaccurate. Almost any schoolboy knows that the circumference of a circle is not the diameter times 3, but rather, the diameter times a well-known constant called ("Pi"). The real value of 7r is 3.14159265358979, but is commonly approximated by 22/7. This is assumed, by many, to be an "error" in the Old Testament record, and is often presented as a skeptical rebuttal to the "inerrancy" of the Scripture. How can we say that the Bible is inerrant when it contains such an obvious geometrically incorrect statement? How do we deal with this?

16. Pi And The Fibonacci Numbers Can we improve Gregory's Formula by making it converge more quickly (i.e. use less terms to get a more accurate value of pi)? http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

17. Solomon's Sea And The Value Of Pi value of pi. © Copyright 2003. Joseph Francis Alward. Bible skeptics allege thatthe writer of 1 Kings couldn t possibly have been inspired because he http://sol.sci.uop.edu/~jfalward/value_of_pi.html

Joseph Francis Alward Bible skeptics allege that the writer of 1 Kings couldn't possibly have been inspired because he evidently believed that the value of pi was 3, not the more nearly correct value of 3.14, but a closer look reveals that if one allows for reasonable "round-off" by the Bible writers, there is no error. E-Mail Alward Home Page The circumference of a circle is obtained by multiplying pi times the diameter. Bible skeptics allege that the writer of 1 Kings couldn't possibly have been inspired because he evidently believed that the value of pi was 3, not the more nearly correct value of 3.14. As evidence, the skeptics point to 1 Kings 7:23 in which the writer says that circumference of Solomon's man-made circular pond was 30 cubits and its diameter was 10 cubits: "He [Solomon] made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it." However, if the circumference of the pond really was 30 cubits, the diameter would have to be 9.549 cubits, approximately. Rounded to the nearest integer, the diameter is 10 cubits, which is close enough, even for a god who could have given the value of

18. Marko Nippula's Home Page Vote On The Future Value Of Pi Vote on the Future value of pi Results http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

19. Yet Another Story Of Pi The next indication of the value of pi occurs in the Bible. Another majorstep towards a more accurate value of pi was taken when the great Archimedes http://www.geocities.com/CapeCanaveral/Lab/3550/pi.htm

The story of pi by Lazarus Mudehwe Undoubtedly, pi is one of the most famous and most remarkable numbers you have ever met. The number, which is the ratio of circumference of a circle to its diameter, has a long story about its value. Even nowadays supercomputers are used to try and find its decimal expansion to as many places as possible. For pi is one of those numbers that cannot be evaluated exactly as a decimal - it is in that class of numbers called irrationals. The hunt for pi began in Egypt and in Babylon about two thousand years before Christ. The Egyptians obtained the value (4/3)^4 and the Babylonians the value 3 1/8 for pi. About the same time, the Indians used the square root of 10 for pi. These approximations to pi had an error only as from the second decimal place. (4/3)^4 = 3,160493827... 3 1/8 = 3.125 root 10 = 3,16227766... pi = 3,1415926535... The next indication of the value of pi occurs in the Bible. It is found in 1 Kings chapter 7 verse 23, where using the Authorised Version, it is written "... and he made a molten sea, ten cubits from one brim to the other : it was round about ... and a line of thirty cubits did compass it round about." Thus their value of pi was approximately 3. Even though this is not as accurate as values obtained by the Egyptians, Babylonians and Indians, it was good enough for measurements needed at that time. Jewish rabbinical tradition asserts that there is a much more accurate approximation for pi hidden in the original Hebrew text of the said verse and 2 Chronicles 4:2. In English, the word 'round' is used in both verses. But in the original Hebrew, the words meaning 'round' are different. Now, in Hebrew, etters of the alphabet represent numbers. Thus the two words represent two numbers. And - wait for this - the ratio of the two numbers represents a very accurate continued fraction representation of pi! Question is, is that a coincidence or ...

20. Buffon S Problem Calculating The Value Of PI Using Toothpicks Calculating the value of pi using toothpicks, to illustrate Count Buffon s problem.A problem for Math 31 or Junior High students. http://www.geocities.com/thesciencefiles/buffon/buffon.html

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